>perl -le "for ('a'..'z') { $h{$_ x 2}=1; print scalar %h }
1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/16
9/16
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11/16
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13/16
14/16
15/16  <- before adding 'pp'
15/16  <- after  adding 'pp'
15/16
15/16
15/16
15/16
21/32
21/32
21/32
21/32
21/32
21/32